The Stacks project

Definition 73.8.1. Let $S$ be a scheme and let $X$ be an algebraic space over $S$. A ph covering of $X$ is a family of morphisms $\{ X_ i \to X\} _{i \in I}$ of algebraic spaces over $S$ such that $f_ i$ is locally of finite type and such that for every $U \to X$ with $U$ affine there exists a standard ph covering $\{ U_ j \to U\} _{j = 1, \ldots , m}$ refining the family $\{ X_ i \times _ X U \to U\} _{i \in I}$.